The father signing away his rights is meaningless unless it happened in a legal proceeding (court case). You can petition for adoption and if, in that context the father signs a relinquishment and the court approves the second parent (you) adoption, the child would become your legal child. The father would then have no further rights unless the adoption included an open adoption agreement/order.
Answered on Oct 02nd, 2013 at 2:23 PM